Low-mass dielectron measurement in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\ \mathrm{TeV}$ with ALICE at the LHC

In ordinary matter, quarks and gluons are confined inside hadrons by the strong interaction. At extreme conditions of temperature and energy density, a new state of matter is formed, called quark-gluon plasma (QGP). This is made of deconfined quasi-free quarks and gluons. Based on the current cosmological picture, the quark-gluon plasma was the state of our universe few $\mu$s after the Big Bang. Moreover, there is evidence that a degenerate state of matter with similar properties to the QGP exists in the inner core of neutron stars and other compact astrophysical objects. \newline \indent Microscopic and extremely short-lived quantities of such a nuclear plasma can be created in ultra-relativistic heavy ion collisions. Its properties can be studied through several experimental probes using dedicated detectors installed around the collision region. This interesting branch of research is part of the experimental program of the Large Hadron Collider (LHC) at CERN, where lead ion beams are accelerated to unprecedented energies. \newline \indent The QGP properties, in principle, can be described by Quantum-Chromo Dynamics (QCD), the quantum field theory of the strong interaction. However, a description of the system based on QCD first principles is extremely complicated due to the relatively low energy scale involved (compared to $\Lambda_{QCD}$), which does not allow to solve the QCD equations using the perturbative approach. Further complications arise from many-body properties of QCD which are anyhow extremely interesting to explore. \newline \indent The deconfined medium created in heavy-ion collisions rapidly evolves, passing through several thermodynamic stages. According to the overall picture of the space-time evolution of the collision, the system quickly approaches local thermal equilibrium. This phase is followed by a rapid expansion, which is usually described by relativistic hydrodynamics. During the system expansion, its temperature and density decrease until quarks and gluons recombine into hadrons. After hadronization, the interactions in the hot and dense gas of hadrons are described using phenomenological transport models. In this stage, the particle density further decreases until all interactions cease at the so-called freeze-out, after which the particles produced propagate freely into the vacuum. \newline \indent Photons and dileptons are unique tools to study the properties of heavy-ion collisions. These particles are continuously emitted by the expanding system, and they cross the medium with negligible final state interaction, thus carrying undisturbed information on their production source. Electromagnetic probes provide complementary information to hadronic probes, which are mostly sensitive to late stages of the collision, thus allowing to constrain the theoretical models used for the description of the system in the early stages. Thermal photons and dileptons carry information on the system temperature. Moreover, in-medium effects of short-lived vector mesons can be studied through their dilepton decay channels. Modifications of the electromagnetic spectral functions of low-mass mesons are expected in a high-temperature and high-density hadronic environment. These modifications, which are reflected in the resonance mass or width, have since long been proposed as signatures of chiral symmetry restoration. Dileptons are also sensitive to heavy-flavor production, which gives a significant contribution to the intermediate mass region of the dilepton spectrum ($m_{\phi} < m_{l^{+}l^{-}} < m_{J /\psi}$). \newline \indent In this thesis, the dielectron production in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\ \mathrm{TeV}$ with the ALICE experiment at the LHC has been studied. ALICE is the detector at the LHC dedicated to the study of heavy-ion collisions. Its excellent tracking and particle identification capabilities, over a wide range of particle momenta, make this experiment well suited for dielectron measurements. A large effort has been dedicated to the suppression of the main sources of background through innovative and efficient techniques. The main focus has been the study of the low-mass region of the dielectron invariant mass spectrum, where contributions from thermal dileptons and from in-medium modified low-mass vector mesons are expected. The fraction of virtual direct photons has been measured, which is compatible with real direct photon measurement from ALICE and existing dielectron measurements from RHIC at lower center-of-mass energy. Moreover, the measured dielectron spectrum has been compared to the expected contributions from hadron decays, thermal dileptons and in-medium modified $\rho^{0}$ and $\omega$ mesons, resulting in good agreement within the experimental uncertainties. The future perspectives for the dielectron measurement and the predicted scenario after the upgrade of the main ALICE sub-detectors are also presented.